Non-ergodic phases in strongly disordered random regular graphs

@inproceedings{BLAltshuler2016NonergodicPI,
  title={Non-ergodic phases in strongly disordered random regular graphs},
  author={B.L.Altshuler and E.Cuevas and L.B.Ioffe and V.E.Kravtsov},
  year={2016}
}
B. L. Altshuler, E. Cuevas, L. B. Ioffe, 4 and V. E. Kravtsov 4 Physics Department, Columbia University, 538 West 120th Street, New York, New York 10027, USA Departamento de F́ısica, Universidad de Murcia, E30071 Murcia, Spain CNRS and Universite Paris Sud, UMR 8626, LPTMS, Orsay Cedex, F-91405, France L. D. Landau Institute for Theoretical Physics, Chernogolovka, Russia Abdus Salam International Center for Theoretical Physics, Strada Costiera 11, 34151 Trieste, Italy 
9 Citations

Figures from this paper

Localization and non-ergodicity in clustered random networks

It is demonstrated that in the main zone the level spacing matches the Wigner–Dyson law and is delocalized, however it shares the Poisson statistics in the side zone, which is the signature of localization, and speculation about the difference in eigenvalue statistics between ‘evolutionary’ and ‘instant’ networks is speculated.

Finite plateau in spectral gap of polychromatic constrained random networks.

It is claimed that at the plateau the spontaneously broken Z_{2} symmetry is restored by the mechanism of modes collectivization in clusters of different colors, and the phenomena of a finite plateau formation holds also for polychromatic networks with M≥2 colors.

Anomalous Thermalization in Ergodic Systems.

It is found that for subdiffusively thermalizing systems the variance scales more slowly with system size than expected for diffusive systems, directly violating Berry's conjecture.

Quantum Ergodicity in the Many-Body Localization Problem.

These results, corroborated by comparison to exact diagonalization for an SYK model, are at variance with the concept of "nonergodic extended states" in many-body systems discussed in the recent literature.

Non-ergodic delocalization in the Rosenzweig–Porter model

We consider the Rosenzweig–Porter model $$H = V + \sqrt{T}\, \varPhi $$H=V+TΦ, where V is a $$N \times N$$N×N diagonal matrix, $$\varPhi $$Φ is drawn from the $$N \times N$$N×N Gaussian Orthogonal

Symmetry violation of quantum multifractality: Gaussian fluctuations versus algebraic localization

Quantum multifractality is a fundamental property of systems such as non-interacting disordered systems at an Anderson transition and many-body systems in Hilbert space. Here we discuss the origin of

Selective state spectroscopy and multifractality in disordered Bose-Einstein condensates: a numerical study

A modified version of the excitation scheme introduced by Volchkov et al. is applied to address the critical state at the mobility edge of the Anderson localization transition, and the projected image of the cloud is shown to inherit multifractality and to display universal density correlations.

References

SHOWING 1-10 OF 12 REFERENCES

Large Deviation Function for the Number of Eigenvalues of Sparse Random Graphs Inside an Interval.

A general method to obtain the exact rate function controlling the large deviation probability Prob[I_{N}[a,b]=kN]≍e^{-NΨ(k)} that an N×N sparse random matrix has I-N eigenvalues inside the interval [a, b].

Random graphs

  • A. Frieze
  • Mathematics, Computer Science
    SODA '06
  • 2006
Some of the major results in random graphs and some of the more challenging open problems are reviewed, including those related to the WWW.

PROOF OF A THEOREM OF A.?N.?KOLMOGOROV ON THE INVARIANCE OF QUASI-PERIODIC MOTIONS UNDER SMALL PERTURBATIONS OF THE HAMILTONIAN

CONTENTS § 1. Introduction § 2. Formulation of the theorems § 3. Proofs § 4. Technical lemmas § 5. Appendix. The rotatory motion of a heavy asymmetric rigid bodyReferences

Mathematical Methods of Classical Mechanics

Part 1 Newtonian mechanics: experimental facts investigation of the equations of motion. Part 2 Lagrangian mechanics: variational principles Lagrangian mechanics on manifolds oscillations rigid

Europhys

  • Lett. 96, 37004
  • 2011

Information

The multifractal statistics was observed also in the numerical study [C. Monthus and T. Garel

  • J. Phys. A
  • 2011

New J

  • Phys. 17, 122002
  • 2015